Liang Hualou, Wang Hongbin
School of Biomedical Engineering, Science & Health Systems, Drexel University, Philadelphia, PA, United States of America.
Center for Biomedical Informatics, Texas A&M University Health Science Center, Houston, TX, United States of America.
PLoS Comput Biol. 2017 Jan 3;13(1):e1005325. doi: 10.1371/journal.pcbi.1005325. eCollection 2017 Jan.
Understanding the relationship between brain structure and function is a fundamental problem in network neuroscience. This work deals with the general method of structure-function mapping at the whole-brain level. We formulate the problem as a topological mapping of structure-function connectivity via matrix function, and find a stable solution by exploiting a regularization procedure to cope with large matrices. We introduce a novel measure of network similarity based on persistent homology for assessing the quality of the network mapping, which enables a detailed comparison of network topological changes across all possible thresholds, rather than just at a single, arbitrary threshold that may not be optimal. We demonstrate that our approach can uncover the direct and indirect structural paths for predicting functional connectivity, and our network similarity measure outperforms other currently available methods. We systematically validate our approach with (1) a comparison of regularized vs. non-regularized procedures, (2) a null model of the degree-preserving random rewired structural matrix, (3) different network types (binary vs. weighted matrices), and (4) different brain parcellation schemes (low vs. high resolutions). Finally, we evaluate the scalability of our method with relatively large matrices (2514x2514) of structural and functional connectivity obtained from 12 healthy human subjects measured non-invasively while at rest. Our results reveal a nonlinear structure-function relationship, suggesting that the resting-state functional connectivity depends on direct structural connections, as well as relatively parsimonious indirect connections via polysynaptic pathways.
理解大脑结构与功能之间的关系是网络神经科学中的一个基本问题。这项工作涉及全脑水平上结构 - 功能映射的一般方法。我们将该问题表述为通过矩阵函数进行结构 - 功能连通性的拓扑映射，并通过利用正则化程序来处理大型矩阵以找到稳定解。我们引入了一种基于持久同调的网络相似性新度量，用于评估网络映射的质量，这使得能够在所有可能的阈值上详细比较网络拓扑变化，而不仅仅是在单个可能并非最优的任意阈值上。我们证明了我们的方法能够揭示预测功能连通性的直接和间接结构路径，并且我们的网络相似性度量优于其他现有方法。我们通过以下方式系统地验证了我们的方法：（1）比较正则化与非正则化程序；（2）度保持随机重连结构矩阵的空模型；（3）不同的网络类型（二元矩阵与加权矩阵）；以及（4）不同的脑部分割方案（低分辨率与高分辨率）。最后，我们用从12名健康人类受试者静息状态下非侵入性测量获得的相对较大的结构和功能连通性矩阵（2514x2514）评估了我们方法的可扩展性。我们的结果揭示了一种非线性结构 - 功能关系，表明静息态功能连通性取决于直接结构连接以及通过多突触途径的相对简约的间接连接。
